In a circle radius 10cm,an arc PQ subtends an angle of radians at the centre of the circle.Calculate the radius of another circle whose circumference is equal to the length of arc PQ
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In a circle of radius 10 with angle θ, PQ = 10θ
So, if circle S has circumference 10θ, its radius is 10θ/(2π)
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Sorry. Number which you deliberately concealed ...
what are u talking about
You say "an angle of radians" without specifying how many radians. It's vital information.
an angle of 2.3 radians?
an angle of π/4 radians?
an angle of √7 radians?
To solve this problem, we need to use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius.
Given that the length of arc PQ is equal to the circumference of the new circle, we can set up an equation:
C(arc PQ) = 2πr(new circle)
Since the length of arc PQ is given, we can substitute it into the equation:
radian measure of arc PQ = r(arc PQ) / r(circle)
Since the radius of the original circle is given as 10 cm, we can substitute this value:
radian measure of arc PQ = r(arc PQ) / 10
Next, we can solve for the radius of the new circle:
r(new circle) = (radian measure of arc PQ) * 10
By substituting the given value of the angle measure, we can calculate the radius of the new circle.